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Some Absolute Properties of A-Computable Numberings

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Algebra and Logic Aims and scope

For an arbitrary set A of natural numbers, we prove the following statements: every finite family of A-computable sets containing a least element under inclusion has an Acomputable universal numbering; every infinite A-computable family of total functions has (up to A-equivalence) either one A-computable Friedberg numbering or infinitely many such numberings; every A-computable family of total functions which contains a limit function has no A-computable universal numberings, even with respect to Areducibility.

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Authors and Affiliations

  1. Al-Farabi Kazakh National University, Al-Farabi Ave. 71, Alma-Ata, Kazakhstan, 050040

    S. A. Badaev & A. A. Issakhov

  2. Kazkh-British Technical University, ul. Tole bi 59, Alma-Ata, Kazakhstan, 050000

    A. A. Issakhov

Authors
  1. S. A. Badaev
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  2. A. A. Issakhov
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Correspondence to S. A. Badaev or A. A. Issakhov.

Additional information

*Supported by the Science Committee of the Republic of Kazakhstan, grant No. AP05132349.

Translated from Algebra i Logika, Vol. 57, No. 4, pp. 426-447, July-August, 2018.

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Badaev, S.A., Issakhov, A.A. Some Absolute Properties of A-Computable Numberings. Algebra Logic 57, 275–288 (2018). https://doi.org/10.1007/s10469-018-9499-0

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  • DOI: https://doi.org/10.1007/s10469-018-9499-0

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